Mathematics for Economists

Cake eating problem

VT 1 (w) = max

c 2 [ 0 ,w]



βT^2 u(c)+VT(wc)



=

= max

c 2 [ 0 ,w]



βT^2 u(c)+βT^1 u(wc)



=

= βT^2 u(c(w))+βT^1 u(wc(w)).

By the envelope theorem if

f(p)$maxx g(p,x)=g(p,x(p))

then

df(p)

dp =

∂g

∂p(p,x(p))+

∂g

∂x(p,x(p))

dx(p)

dp =

∂g

∂p(p,x(p)),